Apparatus for converting light energy from one frequency to another



F254 xv 3,334.433

M H. y 1, 1968 N. BLOEMBERGEN 3,384,433

APPARATUS FOR CONVERTING LIGHT ENERGY FROM ONE FREQUENCY TO ANOTHER Filed July 9. 1962 2 Sheets-Sheet 1 FIG. 1 8

IO :2 :0 l2 :0 l2 IO 2 v f f f m 5i mvsmon Nicoluos Bloembergen AFI'ORNEYS y 1968 N. BLOEMBERGEN 3, 33

APPARATUS FOR convzn'rms men-"r ENERGY FROM ONE FREQUENCY TO ANOTHER Filed July 9, 1962 2 Sheets-Sheet f.

mvzm'oa N icoloos Bloembergen ATTORNEYS United States Patent Oifice 3,384,433 Patented May 21, 1968 $384,433 APPARATUS FOR CONVERTING LIGHT ENERGY FROM ONE FREQUENCY TO ANOTHER Nicolaas Bloembergen, Lexington, Mass. Cruft lgbgratory, Harvard University, Cambridge, Mass.

Filed July 9, 1962, Ser. No. 208,551 8 Claims. (Cl. 350-150) of light waves is identified by the vector quantity t2, "the polarization produced thereby in a dielectric medium is descrihable by the vector quantity '1 which is related to E by the equation I =K l:, wherein K is the dielectric tensor of the medium. For light of the intensities encountered in everyday experience K is for all practical purposes composed of constant terms, independent of the value of E. In fact however, the relation between polarization and electromagnetic wave amplitude is not truly linear, and includes higher powered terms of E. Forhighly intense light beams such as the coherent beams produced by optical masers (hereinafter called lasers), these higher powcred terms, and particularly the terms in the second, third or other low powers of become non'negligible. In con- Sequc'nc'c of this fact. with suitably selected dielectrics and sufficiently intense light waves E, the polarization P in- '--duccd in the dielectric includes a significant second or other higher harmonic component. Under such circumstances the dielectric is said to be non-linear. If the di-' electric is illuminated in the same region thereof with two such intense beams of different frequencies, the induced polarization will include components at their sum and difference frequencies. The case of second harmonic gen' eration may be viewed as a special case of that involving two intersecting beams of unlike frequency, in which however the two beams are brought into coincidence of position and frequency.

The second harmonic sum (or difference) frequency component (hereinafter called the third frequency) of the polarization may under certain circumstances give rise to an electromagnetic (i.e., light) wave in the dielectric. Whether and to what extent this light wave at the third frequency will grow in amplitude to significant levels depends on the phase relations between it and the polarization wave of that sum or difference frequency. Desirably,

for build-up of the third frequency electromagnetic wave, that wave and the third frequency component of thepolarization should everywhere he in a fixed relative phase, ideally in quadrature, with the polarization component lcading. The travelling electromagnetic wave at the third frequency and the travelling polarization wave at the third frequency should therefore. at least ideally, have the same phase velocity in the dielectric, which is equivalent to saying that they should have the same wave number vectors, since their temporal frequencies are equal.

if the third frequency is the sum frequency, the sum frequency component of the polarization wave can he shown to have a spatial variation in the dielectric characterizcd by a wave number vector IT; which is the vector sum of the wave number vectors fiend RT of the incident electromagnetic (hereinafter E .M.) waves E; and ii: of frequencies f, and 1;. The EM. wave at the sum frequency is however characterized by a wave number vector which depends strictly on the index of refraction of the dielectric at the sum frequency. Since except in regions of anomalous dispersion the index of refraction of the dielectric increases with frequency, the wave number vector of the EM. wave at the sum frequency will in nearly every case be greater, in absolute value, than the sum of the absolute values of the wave number vectors of the incident EM. waves ET and Hence it isclear that the wave number vector of the sum frequency EM. .wave must be longer than, and hence cannot coincide with the wave number vector of the sum frequency polar ization wave. The phase velocity of the sum frequency polarization wave will be greater than that of the sum frequency EM. wave, the two will get out of step, and build-up of the sum freqency EM. wave is prevented.

if the third frequency is to be the difference or a higher harmonic or combination frequency, then the wave number vector, 12;, of the third frequency polarization wave can be determined as the vector difference or the corresponding linear combination of wave number vectors of the incident electromagnetic waves. For example, even in the case of a combination of three waves at frequencies it, I: and f4 10 form is, if fa=1t+fr44 The foregoing discussion has assumed the dielectric to I be optically isotropic. It has been proposed heretofore to employ the well-known differences in index of refraction between ordinary and extraordinary rays in a birefringent dielectric material in order to effect. by careful selection of the directions of propagation and planes of polarization of theiand lgwaves through the dielectric, such wave number vectors-for Fraud fig in the material that their vector sum (which characterizes the sum frequency polarization wave) is equal to the wave number vector of the sum frequency EM. wave. In this manner it has been possible to effect a match of the two phase velocities of interesc and to obtain a significant conversion of energy from the incident EM. waves of frequency I, and j; to the EM. wave of frequency 15+),

Such arrangements are however highly critical with respect to the angular orientation of the light sources with respect to the dielectric. Further, they limit the choice of material to one which is strongly birefringent. The present invention proposes instead to achivc a cumulative build-up in the amplitude of the sum frequency EM. wave by periodically shifting or correcting the relative phase of the third frequenrv polarization and EM. waves. The invention will now be described in further detail by reference to the accompanying drawings in which:

FIGS. 1 to 5 are diagrams illustrating separate embodiments of my invention, and FIG. 6 is a diagram useful in explaining the operation of the embodiment of FIG. 1. The embodiment of FIG. 1 is useful when it is desired to generate the simple sum or difference frequency of two incident EM. waves, employing the square-law term in the relation $=KE in the polarization of a non-centre symmetric dielectric.

Referring to FIG. 1, two lasers are indicated diagram- 7 The beams E: and E; are in general but'nced not be oblique to each other, and pass through a common region "published in the Physical Review.

3 of a dielectric mass generally indicated at 8. The mass 8 is composed of a plurality of slabs or lamellae l and 12 which alternate with each other. The slabs may be considered as being seen in plan in H6. 1. All of the slabs l0 and 12'. may be made of the same material, which must be transparent to light of the frequencies f,, j, and 1 or f1Ig. The fact that I; is a'simple sum or simple difference of f and f entails the requirement that the matcrial be nonccntro-symmetric (hereinafter abbreviated as N.C.S.). The material is preferably cubic in crystal lattice. it is also preferably to a first order optically isotropic, but need not necessarily be thus isotropic. and any of the arrangements disclosed here for isotropic materials will also be operative with birefringent materials. Zinc sulfide is a suitable material for light beams F; and E in the visible range. Except for a first slab 10' which is advantageously made substantially half as thick as the others. the slabs mayy all be of the same thickness, and are advantageously made in the form of plane parallel plates. as indicated in the figure.

The slabs 12 differ from the slabs l0 (and the slab 10) between which they are intercalated in that they are, in respect of crystal symmetry, the inversion image of the slabs 10 and 10'.

All materials which are naturally of N.C.S. type exist in two species each of which is the inversion image of the other. In the case of optically active materials such as quartz or sodium chlorate. the two forms are readily identifiable by their dextrorotatory and levorotatory properties. In materials such as zinc sulfide. the two forms may be distinguished on the basis of X-ray diffraction and piezo-electric tests as described for example in the article of C. S. Smith. entitled Sy mmetry and Properties. in volume 6 of Solid State Physics, edited by F. Seitz and D. Turnbull.

Thus in FIG. 1 the slabs 12. to be inversion images of slabs 10. must be composed of the opposite species of N.C.S. material. and oriented so that their crystallographic I axes are parallel to those of slabs l0 and 10'.

In contrast to l\'.C.S. materials. a (5. material is one in which. when its crystal unit cell is inverted through a point called the center of symmetry of the unit cell, the unit cell so inverted is identical with its former self.

'l he directions and planes of polarization of the incident light beams from lasers 2 and 4 with respect to this crystallographic orientation are chosen in such a manner that in the dielectric mass 8 the component of the polarization at the third frequency perpendicular to the direction of propagation of the EM. wave at the third frequency is '10! zero, and preferably is as large as possible.

For example in ZnS both incident beams may propagate along the 111 direction and be polarized along the 110 direction. The polarization wave P; at the third frequency will be polarized along the 001 direction, which has a component perpendicular to the direction of the third wave along Ill, thus satisfying this condition. See Ofiice of Naval Research Contract No. 1866 (32) NR- 371016,-Tecbnical Report on Interactions Between Light Waves in a Non-Linear Dielectric. by .l. A. Armstrong,

N. Bloembcrgen (the applicant) and others of Mar. 20, 1962, constituting Technical Report No. 358 of Cruft Laboratory, Harvard University. Cambridge. Mass, to be The slabs 10 and 12 are so dimensioned, with respect to the frequencies involved and the directions of propagation of the waves therethrough. that the polarization and E.M. waves at the third frequency undergo in the traversal of each slab pha e changes vhich differ by nzl z cycles, It being an integer. With the exception preferably of the first slab It). the slabs may all be of the same thickne s but need not be. and the direction of propagation of the third frequency polarimtion and EM. waves may but need not be normal to the-interfaces between the slabs. in gen eral it will not be so normal.

Depending upon the angles of incidence of the beam E and E: on the outermost face. the thickness of the slabsis selected to hold the difference in phase change between the polarization and EM. waves at the third frequency to the desired value of ni /i cycles. The relationships are indicated in the sketch of FIG. 6 which shows to an enlarged scale the first slab 10'. FIG. 6 has been drawn on .the assumption that the third frequency f, is the sum of the incident wave frequencies f, and In FIG. 6 the light beams E, and E, are shown incident on the slab from the left at unlike angles of incidence. After refraction at the exterior surface of the slab, they progress through the slab in directions and with spatial frequencies identifled by the wave number vectors K and K respectively.

The vector K which is the sum of vectors K and 14 identifies the direction and spatial frequency of the polarization wave P, at the sum frequency f t-h. This polarization wave is incident at an angle on the interface bounding slab 10' on the right. The sum frequency EM. wave F generated by P, is identified in FIG. 6 by means of its wave number vector K which is parallel 'to the vector K but which has typically a different length. K igiven by the equation KjE=(]1+!2)n1" /r, wherein n is the index of slab 10' at the sum frequency and c is the velocity of light in free space.

The wave P gives rise to and amplifies an EM. wave 5;, at the third frequency as long as it is leading this wave in phase. EM. waves of spontaneous origin having suchfrequency and direction that, when overrun by the wave P they possess the proper phase relation with respect to P will absorb energy from P while others may surrender energy to P, or be unaffected by it. The proper phase relation is that in which P leads the EM. wave or waves to be amplified by an angle of from 0 to 180. with maximum transfer of energy from P when the lead is 90". Waves which absorb energy from P are effectively amplified, and there occurs a cumulative build-up, by a geometric progression, of an f-ZM. wave E. at the sum frequency. the energy for which is derived from P and ultimately from E, and E in consequence, in general, P, and E start out at the entering face of slab l0 with P, leading E; by a quarter of a cycle. The build-up, once started. continues as long. as the P, leads E For effective interaction between them. P; and E must be travelling in the same direction; their wave number vectors can therefore be considered to be collinear. The two waves P, and E, thus progress collinearly but typically at unlike phase velocities, as already explained. Their relative phase thus changes as they propagate through the dielectric. When the phase difference between them has changed to such an extent that E; leads P; instead of lagging it. the direction of energy transfer is reversed. In accordance with the invention. the phase relation between C; and P is changed, preferably repeatedly and indeed periodically, and preferably by 180, so as to forestall the decline in amplitude of 5;. In the embodiment of FIG. 1. this change is effected by alternation of the slabs 10 and 12. This construction has the effect of reversing the phase of P, at each inter that; in view of the angles of incidence 'of'beams E, and

E; from the lasers on the first slab 10. the difference in phase change undergone by P, and E5 within that slab is equal or substantially equal to nz /z't cycles. with u an integer. it may be zero. unless the resultant thickness of the slab would be inconveniently small.

The odd /3 cycle is provided by reason of the fact that E; and P; start out A cycle apart at the left or entering face of slab 10', where wave E; arises lagging P, by When the phase difference between F: and P; has changed by another V4 cycle, their relative phase is on the point otshifting into the region where energy will llow from E to I; instead of from P; to E;. as is desired.

The thickness of the succeeding slabs l0 and 12 is selected so that the difference in phase change undergone by P and E within each such succeeding slab is equal or substantially equal to ni /i cycles. in this way, E is held to a relation with P wherein P wherein P leads E by an angle of from 0 to I80". In FIG. 1. on the assumption that 11:0 in both of the expressions ni /i and nzl, slab is shown as being half as thick as the slabs I0, while s abs 10 and 12 are shown all of the same thickness. This is not necessary however. It need not be zero. and need not be the same from slab to slab.

P and E both traverse each slab along the same (generally) oblique path indicated as of length d in FIG. 6, suffering no changes of direction at the internal interfaces. If the difference g-Ts; between their wave number vectors is written AK, the difierence in phase change which the two undergo in traversing the slab is UK. If in addition the thickness of the slab is denoted T. d=T/cos 6, where 0 is'the angle between K and the normal to the interfaces. The desired condition accordingto the invention, for the slabs other than the first slab 10', is that dAK=-n: /& cycles.

There is evidently a multiple infinity of solutions. The

valve of K is however known from the index of refrac- "er the polarizations produced by E and E of which no prior mention has been made. and also of E to all of which the entire mass 8 is isotropic.

P is also rectilinearly propagated through the entire mass. At each interface however its phase is changed by 180'. Hence the phase relation between P; and E is always (assuming n=0) that which accompanies transfer of energy from P to E In any slabs for which n+0, there will nevertheless be a net transfer from P 10 E3.

Th: thicknesses of the slabs need not of course be exactly those required to satisfy the relation d \K=nz /fi cycles. All that is desired is that in each slab there shall be some net transfer of energy from I, to 5;. To insure that this is achieved however, tolerances on the thicknesscs of the slabs must be computed rather as tolerances on the position of each interface reckoned from the first interface. i.c., from the lefthand face of the first slab 10.

Another embodiment of the invention is illustrated a in FIG. 2. The embodiment of FIG. 1 employs throughout the dielectric mass material which is optically nonlinear so that there is everywhere present a third frequency component of polarization which effects interchange of energy with the third frequency EM. wave. In the embodiment of FIG. 2. this restriction is abandoned in favor of what is perhaps a simpler structure, the intercalated slabs serving simply for correctionof the relative phase of the'P and awaits."

In FIG.,2, the lasers 2 and may be the same as those of FIG. I. The dielectric mass. generally indicated at 16. here comprises alternate plane-parallel plate slabs 18 of optically non'linear (but not necessarily N.C.S.) material and slgaiumamc jjer without nonlinearity or non-linsagilygljjlerent froth that of slabs lmthit'first'slabj'fi advantageouslfofhrilf'thethick- R; but of the same material as slabs 18. Thus the slabs l8 and 18 may be made of ammonium dihydrogen phosphate or of ZnS while the slabs 20 may be made of glass.

The embodiment of FIG. 2 may be used even when the non-linear dielectric oltthich slnhs l8 and Hi are made is of a centro symmetric type. in this case the F..M. wave at the second harmonic or sum or dill'crcncc frequency will be generated by an interaction of the quadrupolar type. which is generally weaker than the dipolar interaction in N.C.S. materials.

For generation of third harmonics or combination frequencies of three incident waves. centro-symrnctric crystals can also be used in the embodiment of FlG. 2, operative by the dipolar type of interaction.

The slabs 18 and 18' may be dimensioned in thickness in accordance with the criteria already explained in connection with FIGS. 1 and 6. The slabs 20 are dimensioned, in view of their different indices of refraction for the EM. waves E E, and E, which are different from the corresponding indices of slabs 18 and 18 and in view of the consequent difierenccs in their wave number vectors for E E and the sum thereof, as required to restore the relative phase of E and P; at the entrance to the first slab 18 to that portion of the cycle of relative phases between P, and E wherein energy is transferred from P; to E and not in the opposite direction. The first slab 20 should thus have such a thickness that the F..M. wave E, which was generated in the slab 18' bounding the mass 16 on the left will enter the first slab 18 at that phase, with respect to the phases thereof F, and 8;. as to be, upon entering the first slab 18. lagging the wave P; generated by E; and E in that first slab 18. The amount of lag is preferably made either 0 or as required in view of the relative length of the wave number vectors grand K so that the relative P ase of E and P, may change by half a cycle within the first slab 18 before 5; begins to lead Pg. Slab 18' may be dimensioned in accordance with the criteria discussed for the slab 10' in FIG. 1.

A third embodiment of the invention is illustrated in FIG. 3. In this embodiment. the complete path of the waves over which energy is transferred from the frequencies f, and f: to the third frequency lies within a homogeneous mass of non-linear dielectric, which must be N.C.S.

The mass. indicated at 22. may have the shape of a plane parallel plate with entering and emergent faces 24 and 26. and plane parallel reflecting faces 28 and 30. The faces 24 and 30 may or may not be parallel. and similarly for 26 and 28. but preferably the point of entry of the two beams E, and F, on face 24 should be near the median plane of the plane parallel plate. as shown in the figure for the face 24 (i.c.. approximately half way between the planes of faces 28 and 30).

The embodiment of FIG. 3 is similar to that of FIGS. l and 2 in that there is applied repetitively a correction to the relative phase of the third frequency polarization wave P, and the third frecy'ency EM. wave E By means of this correction a net increase in energy of the E, wave is achieved between each pair of successive corrections.

Essentially. it is desired that the path d of the waves P, and E; between entry of beams E, and E, at face 24 and the first internal reflection at face 30 possess such a length that the difference in phase change undergone by waves P; and E over this path shall be approximately an odd number of quarter cycles.

The correction is obtained by phase change on refiec-..

tion of the collinear P; and E waves at the parallel faces 28 and 30.

For the dimensioning of the mass 22 in respect of the This path has, at each of its reflections at thc faces 28 and 30. equal angles of incidence and reflection. and the path is made up of one or (usually) for than one pass d between the faces 28 and 30. If T is the thickness of the body 22 between faces 28 and 30. T=d cos 0. As in FIG. 1, it is desired that dAK=n: /fi cycles with AK having the same significance as before.

The considerations bearing on the choice of n are already mentioned in connection with FIGS. 1 and 6. If for example n=0. theinterrelation of AK, 0 and T is that cos fl=TAK. Selection of a combination of the inclinations of the faces 24 and 26 to the faces 28 and 30. of the angles of incidence of the laser beams on face 24 and of the thickness T to provide a convenient solution to the equation cos 0=2TAK is a problem in optical engineering thought not to require further discussion here. It may be mentioned however, that it may be desirable to keep small the angles between the beams E and E as they are incident on face 24 in order that they both may illuminate the same volume of material in body 22 over a long path.

The embodiment of FIG. 3 is operative for the reason that. while 5,, E, and E all suffer a 180 phase shift upon each internal reflection at the faces 28 and 30. the

- wa e I: does not. The sign of the amplitude of P being dependent on the product of the signs of E and E, (or, more exactly, of their fundamental frequency polarization waves P and P which are in phase therewith respeclively). change in sign on each of E and E leaves P unchanged in sign. i.e., unchanged in phase. The desired 180 shift in relative phase of E and P, is thus achieved at the end of each path length d.

A fourth embodiment of the invention is illustrated in FIG. 4. In FIG. 4. two lasers 2 and 4 are shown illuminating with beams of light E, and E; a body 40 of optically nonlinear material. seen in fragmentary plan in FIG. 4. The body 40 may be made of any of the materials hereinabove mentioned as possessing the desired properlies for practice of the invention. The material may be either centro-symmetric (C.S.) or non-centro'symmetric t.\'.C.S.). The opposite faces 41 and 43 of the body 40 are constructed as diehroic mirrors 44 and 46 by the application thereto of a plurality of layers of material of alternating high and low index of refraction for energy of the third frequency. as to which the layers are one half wave length thick. The waves E; and E pass to a large extent unrcflected through the dichroic mirror layers. through the body 40 once, and out the other side. In traversing the body they give rise to a component P of polarization at the third frequency. and thus the waveP; develops an EM. wave E also at the third frequency. Light of the third frequency is however substantially reflected by the mirrors 44 and 46. The thickness T of the body 40 is made such that. in conjunction with the angles of incidence of the laser beams on the body, for the wave Es.

The-thickness T is furtber so adjusted that the difference daK between the phase changes undergone by the third frequency polarization wave P; and the wave E in traversing the body once from the entering side at 44 to the emergent side at 46 is equal to viz-A cycles. Fulfillmen. of this condition insures that the wave E, gains in amplitude on each transit from 44 to 46. In returning from 46 to 44. E is so mismatched in phase velocity to I; that there is no interaction between the two.

A fifth embodiment of the invention is illustrated in FIG. 5. Here a body 50 of optically dense linear material is bounded at plane parallel surfaces by bodies 52 and 54 of optically le s dense non-linear material. The body 50 8 may for example be composed of carbon disulphide in liquid form, while the bodies 52 and 54 may be composed of ammonium dihydrogen phosphate (A.D.P.), or potassium dihydrogen phosphate (K.D.P.). Optically linear entrance and exit windows are shown at-56 and S8. The operation of the embodiment of FIG. 5 will be described in terms of doubling of the frequency of a single laser 2 which develops a beam E; of frequency 1 This beam is totally reflected successively at the bodies 52 and 54, with slight penetration into the non-linear material of those bodies at each such reflection. At each such penetration therefore there is generated a double frequency polarization component P and a resulting double frequency E.M. wave E This wave E is generated and radiates into the linear medium 50 as described in Office of Naval Research Contract No. 1866 (I6) NR-372-012, Advanced Research Project Agency Contract RPA-SD-88, Technical Report on Light Waves at the Boundary of Non-Linear Media. by N. Bloembergen (the applicant) and P. S. Pershan, May 15, 1962, constituting Technical Report No. 367, Division of Engineering and Applied Physics. Cruft Laboratory, Harvard University, Cambridge, Mass, to be published in the Physical Review.

The condition for build-up of E, from reflection to reflection is that at each reflection the wave E; shall arrive for reflection in such phase with respect to the wave E from the preceding reflecton that the wave E1, say, generated by E, at the new reflecton will reinfomce the wave E previously generated, after reflection of the latter at the new reflection. Let R; and E be the wave number vectors of E, and E in the linear medium. Let T be the effective thickness of the cell between reflections in the bodies 52 and 54, d the oblique path length between such reflections, 0 the angles of incidence and reflection of the paths d, and Am, and do the phase shifts on reflection for E, and B, respectively, in the event that these are not negligible.

It is then desired that dK =m and that wherein m is an integer and I is an integer, the latter representing the dispersion in index of refraction of the body 50 between the frequencies f, and 213.

It then follows that d(K,-2K,)=I, but

From this relation, with arbitrary choices for (for example) land T, the value of 0 can be determined.

The embodiment of FIG. 5 might take the form of a fiber of glass coated with an optically non-linear material, and the fiber may be of round or other cross section.

In respect of frequencies, optical. light and related terms as used herein denote but are not limited to the frequencies of the infra-red, visible and ultra-violet ranges of EM. radiation. More generally, invention is applicable whenever the wave lengths of the incident and third frequency waves in the non-linear dielectric are small compared to the path lengths in that dielectric, for examplc the path d in any of the embodiments which have been described hereinabove.

Insofar as N.C.S. materials are employed in the prac rice of the invention, as for example in FIG. 1, the materials may be either naturally of N.C.S. type or may be rendered so by the application of an electric field. Thus the embodiment of FIG. 1 might employ for the mass 8 an integral body of CS. non-linear dielectric, with a succession of pairs of electrodes applied to the upper and lower faces thereof (in the figure) and with potential differences of opposite sign between the electrodes of the successive pairs. In general, for the purposes of the invention, electrically induced non-centro-symmetry is equivalent to natural non-centrosymmetry.

The invention has been described herein in terms of a number of preferred embodiments. It is however not limited thereto. The scope of the invention is rather set forth in the appended claims. For example, FIGS. 1 and 2 include initial slabs 10' and 18 of non-linear-dielectrie having a thickness such that the difference in phase change therethrough of the P, and E waves is an odd number of quarter cycles. This description has been made on the assumption that no wave of frequency 1, was initially available. In applications of the invention as n pixfielrs instead of oscillators, as for example in providing a p ametric con erEPwhether upwards or downwards in sary.

l claim:

1. Apparatus for generating an electromagnetic wave E of a frequency 1, from a plurality of electromagnetic waves E,, E of frequencies 1,, 1 which freqtuncies 1,, 1,. may be equal, and which frequency 1 is a linear combination of the frequencies 1,,'1;, said apparatus comprising a body of non-linear dielectric matezial, a plurality of light sources of frequencies 1,, 1g.

respectively. said sources being positioned to illumina:e a common region of said body. said sources being of sufficient intensity to generate in the body polarizations "taming non-linearly with their intensities, said sources giving rise in said region to a polarization wave of the frequency 1;, and having a wave number vector which is a linear combination of the wave number vectors of the electromagnetic waves in said region from said sources. said body having a plurality of boundaries encountered by said polarization wave. said boundaries successively encountered by said polarization wave being separated by path lengths for said polarization wave over which the difference between the phase change undergone by said polarization wave and the electromagnetic wave of frequency 1;, whose Wave number vector is collinear with that of said polarization wave amounts to substantially ni /'2 cycles. n being an integer.

2. Apparatus for doubling the frequency of alight beam comprising an optical maser adapted to develop an intense coherent monochromatic beam of light of 1, frequency, a body of non-centro-symmetric dielectric material having at 1, a high dielectric constant and a magnetic susceptibility approaching that of free space. the dielectric constant of said body being a non-linear function of the intensity of incident eleetrornagnetic'radiation and including components in higher powers of that 'intensity. whereby upon illumination of said body by an electromagnetic wave E, of frequency 1, there is developed in the body a polarization wave P, of frequency 21,.

said body be ng disposed in position to be illuminated by said maser, and means to shift by substantially the relative phase of P and the electromagnetic wave E, of frequency 21-, developed within said body by P, at points in the path of the waves P, and E, where in said body the difference in phase change undergone thereby is substantially ni /i cycles. n being an integer.

3. A paratus for gepemtg an electromagnetic wave E, of frequency 1 from electromagnetic waves of frequencies 1, and 1,. which may be equal. I; being a linear combination of 1, and 1,. said apparatus comprising a lurality of slabs of non-centro-syrnmetric optically nonlinear dielectric material having substantial transparency and optical isotropy to electromagnetic vtuives til t'tequencies 1,. 1 and 1 adjacent of said sltt'c-s being in rcspect of ctystal symmetry the inversion images of each other, at least one high intensity source of light beam E, of frequency 1, disposed in position to illuminate a common region of said slabs in directions transverse to the long dimension of said slabs, each of said sources having an intensity sufiicient to generate in said body a polarization wave including a component varying according to a power of said intensity higher than the first power. the said beam undergoing refraction on entry into said material into a beam identified as to direction and wave number by a wave number vector K said refracted beam giving rise in said material to a polarization wave P; at frequency f, and identified as to direction and wave number by a wave number vector 14 the first of said slabs having in the direction of K such thickness that the difference in phase change undergone in traversal of that first slab by the wave P and by the electromagnetic wave E generated thereby is substantially ni /1t cycles and the remainder of said slabs having in that direction such thickness that the difference in said phase change undergone therein is substantially ni /5 cycles, n being an integer which may be zero and which may vary from slab to slab.

4. Apparatus for generating an electromagnetic wave E of frequency 1;, fFBTrT'electromagnetic waves of frequcncics 1, and 1:, said apparatus comprising a plurality of plane parallel slabs of non-centro-symmetric dielectric ma:.erial of cubic crystal lattice having substantial transparency and optical isotropy to electromagnetic waves of frequencies 1,, 1 and 1,, adjacent of said slabs being in respect of crystal symmetry the inversion images of each other. being in optical contact with each other. and having their crystallographic axes substantially parallel, the electric polarizability of said material including terms in the second or higher powers of the amplitude of the electric vector of electromagnetic waves passing therethrough, separate high intensity sources of light beams E, and E of frequencies 1, and f said beams E, and E, being of sufiicient intensity to generate in said slabs polarization waves including at least one of said terms. said sources being disposed in position to illuminate a common region of said slabs in directions transverse to the plane parallel faces thereof. the said beams undergoing refraction on entry into said material into beams identified as to direction and wave number by wave number vectors K and K respectively. said refracted beams giving rise in said material to a polarization wave P, at frequency 1, and identified as to direction and wave number by a wave numbervector K derived by combination of the vecthe wave number vector KK and the wave number vector of an electromagnetic wave E, of frequency 1, parallel to the wave P, is substantially equal to ni /4 cycles for the first slab and ni /i cycles for the other slabs, n being an integer which may be zero and which may vary from slab to slab and d being variable from slab to slab.

5. Apparatus for generating an electromagnetic wave E, of frequency 1, from electromagnetic waves of frequencies 1, and 1,. said apparatus comprising a succession of first slabs of optically non-lineardielectrie material having substantial transparency and optical isotropy to electromagnetic waves of frequencies 1,. I; and 1,, adiacent of said first slabs being separated by second slabs of dielectric material of optical linearity different from that of said first slabs. separate high intensity sources of light beams E, and E, of frequencies 1, and disposed 1 1 in position to illuminate a common region of said slabs in directions transverse to the plane parallel faces thereof, said beams being of sufficient intensity to generate in said first slabs polarization waves including at least one term varying with a power of the intensity of said beams higher than the first power, the said beams undergoing refraction on entry into the material of said first slabs into beams identified as to direction and wave number by wave number vectors K and K respectively, said rcfracted beams giving rise in said material to a polarization wave P; at frequency f; and identified as to direction and wave number by a wave number vector K derived by combination of the vectors K and R the first of said first slabs having in the direction of Kgp such thickness that the difference in phase change undergone n traversal of that first slab by the wave P, and by the electromagnetic wave 13;, generated thereby is substantiully ItiA cycles and the remainder of said first slabs ing from said second slabs individually.

6. Apparatus for generating an electromagnetic wave E of frequency from electromagnetic waves of frequencies f, and 1;, said apparatus comprising a body of optically non-linear non-centro-symmetric dielectric material having opposed smooth faces at which total internal reflection may take place. separate high intensity sources of light beams E, and E of frequencies 1 and I3 incident on a common region of said body at inclinations such as enter said body and give rise therein to refracted beams identified as to direction and wave numher by wave number vectors K and K respectively. said beams being of intensity sufficient to generate in said -body polarization waves including a component varying according to a power of that intensity higher than the first, said refracted beams giving rise in said material to a polarization wave P at frequency I; and identified as to direction and wave number by a wave number vector K; derived by combination of the vectors i; and said body being dimensioned to provide for said wave P a path d of such length between entry of beams E and E therein and the first total internal reflection of wave P that the difference in phase change undergone over path 11' by the wave P and by the electromagnetic wave E generated thereby is substantially nil 4 cycles. said body being further dimensioned to provide for said wave P between successive internal reflections therein paths 0' over which the said difierence in phase change is substantially nz'b cycles, n being an integer which may be zero and which may vary from path to path.

12 7. Apparatus for generating an electromagnetic wave E of frequency I; from electromagnetic waves of frequencies f; and 1 said apparatus comprising a body of optically non-linear dielectric material having two plane parallel faces, separate high intensitysources of light beams E and E of frequencies 1, and f incident on a common region of said body transversely of said faces,

said beams being of intensity sutficient to generate in said body polarization waves including a component varying according to a power of that intensity higher than the first, and a dichroic mirror on each of said faces having low reflectance to the frequencies f and I; and higher reflectance to the frequency 1 derived as a linear combination of the frequencies 1 and ,2, the thickness of said body between said aces being such that for the polarization wave P, of frequency i generated therein by said beams E, and E and for the electromagnetic wave 5; of

'frequency f; generated therein by P the difference in phase change undergone by P and E; in traversing the body between said faces in direction generally parallel to that of the incident light from said sources is substantially' equal to n-Jz'h' cycles, n being an integer which may be zero.

8. Apparatus for generating an electromagnetic wave E; of frequency 2], from electromagnetic waves of frequency 1 said apparatus comprising a body of optically linear material having two opposite plane parallel faces. separate bodies of optically non-linear material disposed in optical contact with each of said faces, and at least one high intensity source of light of frequency 7', disposed in position to send a beam E, into said body for successive reflections at said bodies of non-linear material for generating at each such reflection a polarization wave of frequency 21;. said hcarn being of intensity sufiicicnt to generate in said bodies of non-linear material polarization waves including a component varying according to a power of that intensity higher than the first.

References Cited Bass et al: Optical Mixing. Physical Review Letters, vol. 8, No.1,.lan. 1,1962, p. 18.

Fraulten et 81: Generation of Optical Harmonics," Physical Review Letters, vol. 7, No. 4, Aug. 15, 1961, pp. 119, 120.

Giordmaine: Mixing of Light Beams In Crystals," Physical Review Letters, vol. 8, No. 1, Jan. 1, 1962, pp. 19, 20.

Maker ct al: Effects of Dispersion and Focusing on the Production of Optical Harmonics," Physical Review Letters, vol. 8, No. 1, Jan. 1, 1962, pp. 21, 22.

JEWELL H. PEDERSEN, Primary Examiner.

RONALD L. WIBERT, Examiner. 

1. APPARATUS FOR GENERATING AN ELECTROMAGNETIC WAVE E3 OF A FREQUENCY F3 FROM A PLURALITY OF ELECTROMAGNETIC WAVES E1, E2,... OF FREQUENCIES F1, F2,... WHICH FREQUENCIES F1, F2,... MAY BE EQUAL, AND WHICH FREQUENCY F3 IS A LINEAR COMBINATION OF THE FREQUENCIES F1, F2,... SAID APPARATUS COMPRISING A BODY OF NON-LINEAR DIELECTRIC MATERIAL, A PLURALITY OF LIGHT SOURCES OF FREQUENCIES F1, F2, ... RESPECTIVELY, SAID SOURCES BEING POSITIONED TO ILLUMINATE A COMMON REGION OF SAID BODY, SAID SOURCES BEING OF SUFFICIENT INTENSITY TO GENERATE IN THE BODY POLARIZATIONS VARYING NON-LINEARLY WITH THEIR INTENSITIES, SAID SOURCES GIVING RISE IN SAID REGION TO A POLARIZATION WAVE OF THE FREQUENCY F3 AND HAVING A WAVE NUMBER VECTOR WHICH IS A LINEAR COMBINATION OF THE WAVE NUMBER VECTORS OF THE ELECTROMAGNETIC WAVES IN SAID REGION FROM SAID SOURCES, SAID BODY HAVING A PLURALITY OF BOUNDARIES ENCOUNTERED BY SAID POLARIZATION WAVE, SAID BOUNDARIES SUCCESSIVELY ENCOUNTERED BY SAID POLARIZATION WAVE BEING SEPARATED BY PATH LENTHS FOR SAID POLARIZATION WAVE OVER WHICH THE DIFFERENCE BETWEEN THE PHASE CHANGE UNDERGONE BY SAID POLARIZATION WAVE AND THE ELECTROMAGNETIC WAVE OF FREQUENCY F3 WHOSE WAVE NUMBER VECTOR IS COLLINEAR WITH THAT OF SAID POLARIZATION WAVE AMOUNTS TO SUBSTANTIALLY N+-1/2 CYCLES, N BEING AN INTEGER.
 8. APPARATUS FOR GENERATING AN ELECTROMAGNETIC WAVE E3 OF FREQUENCY 2F1 FROM ELECTROMAGNETIC WAVES OF FREQUENCY F1, SAID APPARATUS COMPRISING A BODY OF OPTICALLY LINEAR MATERIAL HAVING TWO OPPOSITE PLANE PARALLEL FACES, SEPARATE BODIES OF OPTICALLY NON-LINEAR MATERIAL DISPOSED IN OPTICAL CONTACT WITH EACH OF SAID FACES, AND AT LEAST ONE HIGH INTENSITY SOURCE OF LIGHT OF FREQUENCY F1 DISPOSED IN POSITION TO SEND A BEAM E1 INTO SAID BODY FOR SUCCESSIVE REFLECTIONS AT SAID BODIES OF NON-LINEAR MATERIAL FOR GENERATING AT EACH SUCH REFLECTION A POLARIZATION WAVE OF FREQUENCY 2F1, SAID BEAM BEING OF INTENSITY SUFFICIENT TO GENERATE IN SAID BODIES OF NON-LINEAR MATERIAL POLARIZATION WAVES INCLUDING A COMPONENT VARYING ACCORDING TO A POWER OF THAT INTENSITY HIGHER THAN THE FIRST. 